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This section includes 7 InterviewSolutions, each offering curated multiple-choice questions to sharpen your Current Affairs knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Evaluate the following integrals. intsqrt(1+3x-x^(2))dx |
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| 2. |
If f(x)=|{:(x,cosx,e^(x^2)),(1,2 cosx,1),(0,1,2 cosx):}| then the value of overset(pi//2)underset(-pi//2)int f(x) dx is equal to |
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Answer» 0 |
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| 3. |
Verify the Rolle's theorem for each of the function in following questions: f(x)= sqrt(4-x^(2)), "in " x in [-2, 2] |
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| 4. |
Define a vector from the geometrical concept. |
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| 5. |
Let z_(1)=(2sqrt(3)+ i6sqrt(7))/(6sqrt(7)+ i2sqrt(3))" and "z_(2)=(sqrt(11)+ i3sqrt(13))/(3sqrt(13)- isqrt(11)). Then |(1)/(z_1)+(1)/(z_2)| is equal to |
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Answer» `47` |
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| 6. |
Find the unit vector in the direction of veca=hati-2hatj, also find the vector whose magnitude is 7 units and in the direction veca. |
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| 7. |
Find the equation of line passing through the given points using determinants (7,8),(5,-2) |
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| 8. |
x+y-2z=5 x-2y+z=4 -2x+y+z=4 |
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| 9. |
Eleven pirates find a treasure chest. When they split up the coins in it, they find that there are 5 coins left. They throw one pirate overboard and split the coins again, only to find that there are coins left over. So, they throw another pirate over and try again. This time, the coins split evenly. What is the least number of coins there could have been ? |
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| 10. |
Let A={a,b,{a,b}}, where P(A) is the power set of A, then which of the following is/are true? |
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Answer» `B in C` |
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| 11. |
Two circlesx^(2) + y^(2) - 2x + 6y + 6 = 0 " and " x^(2) + y^(2) - 5x + 6y + 15 = 0 touch each other A limiting point of the co-axal system determined by them is |
| Answer» ANSWER :D | |
| 13. |
Integrate the functions (sinx)^(2) |
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| 14. |
Match the following |
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Answer» a,b,C,d |
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| 15. |
If R is a relation on the set A={1,2,3,4,5,6,7,8,9) given by xRy y =3x then R= |
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Answer» {(3,1),(6,2),(9,3) |
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| 16. |
Find the values of the following integrals int_(-3)^(3) (9-x^(2))^(3//2)dx |
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| 18. |
Match the following |
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Answer» a,b,d,e |
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| 19. |
Match the following |
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Answer» d,a,B |
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| 20. |
Match the following |
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Answer» a,b,C,d |
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| 22. |
Match the following |
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Answer» a,c,B,d |
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| 23. |
Two natural numbers r, s are drawn one at a time, without replacement from the set S = {1, 2, 3, 4, ....., n}. Find P(r le p//s le p), where p in S. |
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| 24. |
A bag contains 5 red marbles and 3 black marbles. Three marbles are drawn one by one without replacement. What is the probability that atleast one of the three marbles drawn be black, if the first marble is red ? |
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| 25. |
A thermodynamic study of AlCl_(3(s)) is done to determine its standard enthalpy of formation (Delta_(f)H_(AlCl_(3)(s))^(@)) from the following information. (i) AlCl_(3)(s)s to AlCl_(3) [aq. In 4.0 M-HCl(aq)],DeltaH^(@)=-180 kJ (ii)Al(s)+3HCl (aq.,4.0M) to AlCl_(3) [aq. in 4.0 M-HCl(aq.)]+(3)/(2)H_(2)(g),DeltaH^(@)=-700kJ (iii)(1)/(2) H_(2)(g) +(1)/(2)Cl_(2)(g) to HCl(aq. , 4.0 M), DeltaH^(@)=-158 kJ Determine |Delta_(f)H_(AlCl_(3)(s))^(@)| in kJ from these data: |
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Answer» SOLUTION :[0994] From (ii)+3`XX`(III)-(i),`|DELTAH^(@)|=(-700)+3(-158)-(-180)=+994 kJ//mol` |
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| 26. |
The solution of (dy)/(dx) -y tan x = e^(x) sec x is |
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Answer» `y E^(X) = COS x + C` |
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| 27. |
Let P(n):2^(n_gtnAAn in N and 2 gt k, Aan =k, then which of the following is true? (kge2) |
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Answer» `2^(k)gt5kgt1` |
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| 28. |
If tan^(-1)(x^(2)+y^(2))=alpha then (dy)/(dx) is equal to |
| Answer» ANSWER :A | |
| 29. |
Show that 1/(1.2)+(1.3)/(1.2.3.4)+(1.3.5)/(1.2.3.4.5.6)+...=sqrte-1 |
| Answer» SOLUTION :L.H.S= `1/1.2+1.3/(1.2.3.4)+(1.3.5)/(1.2.3.4.5.6)+...=(1/2)+(1/2)^2/(2!)+(1/2)^3/(3!)+...(1+1/2+(1/2)^2/(2!)+(1/2)^3/(3!)+...)-1=E^(1/2)-1=sqrte-1` | |
| 30. |
If the plane (x)/(a)+(y)/(b)+(y)/(c )=3 meets the coordinate axes in A, B, C, and the centroid of the triangle ABC is at P(2,4,8), then a, b, c are in |
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Answer» A.P |
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| 31. |
int(sin 2x)/(sin^(2)x + 2 cos^(2)x) dx = |
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Answer» `-LOG(1+sin^(2)X) + C` |
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| 32. |
int(e^(2sin^(-1)x))/(sqrt(1-x^2))=dx= |
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Answer» `1/2E^(2sin^(-1)X)+C` |
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| 33. |
Method of integration by parts : intsin^(5)xdx=-(sin^(4)xcosx)/(5)+Asin^(2)xcosx+Bcosx+c then the value of A+B is ......... |
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Answer» `-(2)/(3)` |
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| 34. |
Define a function phi : N to N as follows : phi(1)=1,phi(P^(n))=P^(n-1)(P-1) if P is prime and n in N and phi("mn")=phi(m)phi(n) if m & n are relatively prime natural numbers phi(8n+4) where n in N is equal to |
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Answer» `2phi(4n+2)` |
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| 35. |
If z=(lamda+3)+isqrt(5-lamda^2)then the locus of z is a circle with centre at |
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Answer» (0,0) |
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| 36. |
If a=i+2j-3k, b=2i+j-k then the vector v satisfying a times v=a times b" and "a*v=0" is "b+ta,t being a scalar for |
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Answer» all VALUES of t |
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| 37. |
Form the differential equations of the following families of curves by elimnating the parameters (arbitrary constants) given against them in the brackets. (i) y = c(x-c)^(2), (c) (ii) xy = a e^(x) + b e^(-x), (a, b) (iii) y = (a+bx)e^(Kx), (a,b) (iv) y = a cos (nx + b), (a,b) (v) = y = a e^(3x) + be^(4x), (a,b) (vi) y = ax^(2) + bx, (a,b) (vii) ax^(2) + by^(2) = 1 (a,b) |
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Answer» (ii) `x(d^(2)y)/(dx^(2)) + 2(dy)/(dx) - xy = 0` (iii) `y_(2) - 2ky_(1) + k^(2)y = 0` (iv) `y_(2) + n^(2)y = 0` (V) `y_(2) - 7y_(1) + 12y = 0` (vi) `x^(2)(d^(2)y)/(dx^(2)) - 2X(dy)/(dx) + 2y = 0` (vii) `xy y_(2) + xy_(1)^(2) - y y_(1) = 0` |
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| 38. |
Let f(x)=cos3x+sinsqrt(3)x. Then f(x) is : |
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Answer» a PERIODIC function of PERIOD `2pi` |
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| 39. |
Find the approximate value of each of the following :tan 31^(@) |
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| 40. |
Method of integration by parts : int(x-sinx )/(1-cosx)dx=.... |
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Answer» `X COT((x)/(2))+C` |
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| 41. |
Write down the matrix [[a_11,a_12,a_13],[a_21,a_22,a_23]]"if"a_(ij)=2i+3j |
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Answer» SOLUTION :`a_(IJ)=2i+3j` `:.[[a_11,a_12,a_13],[a_21,a_22,a_23]]=[[5,8,11],[7,10,13]]` |
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| 42. |
A point on the hypotenuse of a triangle is at distance a and b from the side of the triangle.Show that the minimum length of the hypotenuse is (a^((2)/(3))+b^((2)/(3)))^((3)/(2)). |
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| 43. |
Integrate the functions sec^(2)(7-4x) |
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| 44. |
The probability that a student is not a swimmer is (1)/(5). Find the probability that out of 5 students. at most three are swimmers. |
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| 46. |
The solution of the differential equation (dy)/(dx)=sin(x+y)tan(x+y)-1 is |
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Answer» `X + cosec(x+y) = c` |
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| 47. |
PQ and RS are two vertical towers of the same height where S is on the ground Q is above the ground. The line joining the top P and the foot S of the two towers meets the horizontal line through Q at a point A where the angles of elevation of the tops P and R of the two towers are alpha and beta respectively. If AS = a, the height of the towers is |
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Answer» `(a SIN (BETA + ALPHA))/(COS beta)` |
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| 48. |
Consider the following statement I. "Every rectangle is a square" is a statement. II. "Close the door" is not a statement. Choose the correct option. |
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Answer» Only I is false. |
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| 49. |
Show that functions f and g defined by f(x)=2 log x and g(x)=log x^2 are not equal even though log x^2 =2 log x. |
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Answer» Solution :`F(X)=2 "log"x` `g(x)="log" x^2` `"DOM" f(x) = (0,oo)` `"Dom" g(x) =R-{0} ` `"As Dom" f(x) != Dom g(x) "we have" f(x) !=g(x), "though log" x^2 =2"log"x` |
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| 50. |
Given g(x)=(x^2+7/9)/(x^3+11/27), what is g(1/3) ? |
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Answer» `216/243` |
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